Problem of the Week: Valentine’s Day
Editor’s Note: The Department of Mathematics at Gettysburg College hosts a problem of the week challenge to determine each semester’s Paul Mugabi problem-solving award recipient(s). Each week’s entries are scored by a faculty judge, and winner(s) from each week will receive a Problem Of the Week (P.O.W.) button. The Gettysburgian is not involved in or responsible for accepting or evaluating students’ submissions to this contest.
THE RULES:
The contest is open to all Gettysburg College students. Up to three people may work together on a submission. Make sure your name is on your submission and that any sources are properly cited. Send solutions to bkennedy@gettysburg.edu. This problem was posted on Friday, February 18 and solutions are due on Friday, February 25 by 5:00 p.m.
THE PROBLEM:
For Valentine’s day, I ordered myself a candy-of-the-week subscription from Scrumptious Sweets. Scrumptious Sweets makes 4 kinds of candy. Every week, they will randomly select one kind of candy to send me (regardless of what they have sent me before).
THE QUESTION:
After how many weeks will it be more likely than not that I have received every kind of candy at least once? Answer, and explain.
Can you generalize to the situation that Scrumptious Sweets makes n kinds of candy?
